For creativity in problem solving, if the problem is well defined, I've found that light physical activity has been useful for clearing my mind and returning to the task with a refreshed perspective.

When coming up with inspiration I usually try to think backwards. Backwards in the sense that I might start with some idea which is concrete and, start considering it's more abstract forms. So, for example I would consider a pencil as a concrete thing. I might start considering writing instruments. I might then start considering HIDs. From there that's a big world to explore.